Simplify; express your answer in exponential form. Assume $q\neq 0, a\neq 0$. $\dfrac{{(q)^{2}}}{{q^{-1}a^{-4}}}$
Explanation: To start, try working on the numerator and the denominator independently. In the numerator, we have ${q}$ to the exponent ${2}$ . Now ${1 \times 2 = 2}$ , so ${(q)^{2} = q^{2}}$ In the denominator, we can use the distributive property of exponents. ${q^{-1}a^{-4} = q^{-1}a^{-4}}$ Simplify using the same method from the numerator and put the entire equation together. $\dfrac{{(q)^{2}}}{{q^{-1}a^{-4}}} = \dfrac{{q^{2}}}{{q^{-1}a^{-4}}}$ Break up the equation by variable and simplify. $\dfrac{{q^{2}}}{{q^{-1}a^{-4}}} = \dfrac{{q^{2}}}{{q^{-1}}} \cdot \dfrac{{1}}{{a^{-4}}} = q^{{2} - {(-1)}} \cdot a^{- {(-4)}} = q^{3}a^{4}$.